Fitting code for Di Martino et al 2023

1. Model 1: implicit toxicity

In the first model (model 1), we do not have any information on what causes the toxicity of linoleic acid towards At. Based on the experimental growth curves, we know that the toxicity of linoleic acid is not immediate: at a high LA concentration, At first grows at higher levels than explained by the minimal medium growth and then dies after 3 days. We then assume a simple linear accumulation of toxicity over time.

We first start by fitting the minimal medium growth curves.

1.1 Fitting growth in the minimal medium

1.2 Fitting At monoculture parameters

## Goodness of fit of monocultures (sum of errors):
#sum(ssqAtMonoAcc(coef(fitAt))^2)

To be symmetrical between the two bacteria we also assume the same model of toxicity accumulation for Ct, even though LA does not seem to be toxic for Ct.

1.3 Fitting Ct monoculture parameters

        rc         Kc         Yc       beta      gamma 
 0.3996774 -3.0562934  9.1405722 -0.5096482 -5.2840669 

1.4 Comparing co-culture prediction with co-culture data

What about the co-culture prediction?

Error of model 1:

[1] "Sum of errors at 0.1%:  29.8969138718"
[1] "Sum of errors at 0.75%:  460.695978031655"
[1] "Sum of errors:  490.592891903455"

1.5 Parameter set of the main text

[1] "Sum of errors at 0.1%:  25.3958719552748"
[1] "Sum of errors at 0.75%:  457.594456582311"
[1] "Total sum of errors:  482.990328537586"

2. Model 2: explicit toxicity with ROS data

We import the new data of this second experiment.

2.1 Fitting growth in MM

Again we first fit the MM parameters by using both mono- and co-cultures in the no-LA condition. We perform again the fitting because the data has changed (new experiment).

2.2 Fitting ROS spontaneous dynamics in LA medium

2.3 Fitting At monoculture parameters

2.4 Fitting Ct monoculture parameters

2.5 Comparing co-cultures and mono-cultures

[1] "Sum of errors at 0.1%:  67.3249478912224"
[1] "Sum of errors at 0.75%:  168.356800912907"
[1] "Total sum of errors:  235.681748804129"

2.6 Parameter set of the main text

[1] "Sum of errors at 0.1%:  70.4431745694874"
[1] "Sum of errors at 0.75%:  77.5581367404796"
[1] "Total sum of errors:  148.001311309967"

2.7 Example of transfer trajectory

coex = read.delim("Model2_cocult_5.txt")
coex$finstate = as.factor(coex$finstate)
mod2_5transf=ggplot(data=coex, mapping = aes(x =LA_initialconc , y = dilu, fill=finstate)) +
  geom_raster(aes(fill = factor(finstate))) +
  scale_color_manual(values=c(colCt[4],"grey","pink","darkgreen"),
                     aesthetics = c("colour", "fill"),
                     name = "Species surviving after 5 transfers",
                     labels=c("Ct alone", "Extinction of both", "Coexistence: Ct and At", "At alone"),
                     breaks=c("Ct","ext","coex","At")
  ) +
  ylab(expression("Transfer dilution rate")) +
  xlab(expression("Initial linoleic acid concentration"))+
  theme(text = element_text(size=15)) +
  labs(title = "Model 2") +
  theme(plot.title = element_text(size = 15))+
  theme(aspect.ratio=1)
mod2_5transf